• # question_answer                 A point Q lies on die perpendicular bisector of an electrical dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole) then electric field at Q is proportional to: A)                                                                                                                                                                            ${{p}^{-1}}$ and ${{r}^{2}}$    B)                 $p$ and ${{r}^{-2}}$                   C)                 ${{p}^{2}}$ and ${{r}^{-3}}$                    D)                 $p$ and ${{r}^{-3}}$

Electric field due to a dipole at bisector or at a point on its broad side on position is given by                 $E=\frac{1}{4\,\pi {{\varepsilon }_{0}}}.\frac{p}{{{r}^{3}}}$                 or            $E\propto \,\,\frac{p}{{{r}^{3}}}$                                           ....(i)                 where r is the distance of that point from centre of dipole.                 So, from Eq. (i)                 $E\propto \,p$                 and       $E\propto \,{{r}^{-3}}$                 Note:    The electric field due to a dipole at its end on position is twice the value at its broad side on position i.e.,                 ${{E}_{end-on}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{2p}{{{r}^{3}}}$